A good recipe for brown sugar frosting from King Arthur Flour mixes brown sugar with butter, milk, vanilla extract and confectioners' sugar. Another well-regarded recipe for brown sugar frosting is available from Epicurious. Both recipes received great ratings and positive reviews.
Make brown sugar frosting by warming 7 tablespoons of unsalted butter in a pan and stirring in 2/3 cup of brown sugar and 1/4 teaspoon of salt. When the mixture develops a smooth texture, pour in 1/4 cup of milk, and bring the sauce to a boil. Allow the sauce to cool in a bowl for 10 minutes before adding 3/4 teaspoon of vanilla extract and 2 1/4 cups of confectioners' sugar. Whisk the mixture thoroughly to form the frosting. Add more confectioners' sugar to thicken it further if necessary.
Make Epicurious' brown sugar frosting by beating 12 ounces of cream cheese and 3/4 cup of unsalted butter with an electric mixer. When the mixture is soft and light, incorporate 3/4 cup of brown sugar. Gradually beat in 2 1/4 cups of powdered sugar. Add 1 1/2 tablespoons of orange juice concentrate and 1 1/2 teaspoons of vanilla extract. Store the frosting in the refrigerator for approximately 30 minutes to bring it to an ideal consistency.